19. What is the cardinality of each of these sets? b) {{a}} d) {a, {a}, {a, {a}}} a) {a} c) {a, {a}}

Q: How many subsets of the set {1,2,3,4,5,6,7,8} have cardinality 3 or less?

A: Here we need to find how many subsets of the set A={1, 2,3,4,5,6,7,8} have cardinality 3 or less so…

Q: What set is in another class of infinity that is bigger than R?

A:

Q: Use double set inclusion to prove that dep. PANB) = P(A)n P(B).

A: The problem is related with power set P of sets. Here, we have to show that P A ∩ B = P A ∩ PB using…

Q: Suppose S is a set with cardinality n. What is the cardinality of the power set of S ? Are there any…

A: Suppose S is a set with cardinality n. Then power set of S contains 2n elements . Power set of any…

Q: Let A be the set of even positive integers less than 40 and divisible by 4. What is the cardinality?

A: This is the question from set theory.

Q: Prove that the set of irrational numbers has the cardinality of R.

A: In informal terms, the cardinality of a set is the number of elements in that set. If one wishes to…

Q: Suppose that S is a non-empty finite set. Prove that ? has as many even-sized subsets as it does…

A: Let S be a non-empty set. Let A be the set of even sized subsets of S and let B be the set of odd…

Q: Let A = {distinct letters occurring in the word HIPPOPOTAMUS}. What is |A|, the cardinality of the…

A: Cardinality of a set is defined as the number of distinct element in that set.

Q: 4. Any non-empty set A and its power set P(A) do not have the same cardinality (i.e. there exists no…

A:

Q: How many subsets of {0, 1, ...,9} have cardinality 5 or more?

A:

Q: Let A= {1,2,3,4,5,6} and B={2,4,6,8}. what is the cardinality of A ∩ b?

A: Cardinality of a intersection

Q: 5. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

A:

Q: Investigate and illustrate the cardinality of the sets of odd numbers, ?, and ℤ, which properly…

A:

Q: d. What is the cardinality of a countably infinite set?

A:

Q: Suppose A and B are finite sets. Prove or disprove: (aun-aun)- (AUB) = (A u B) ) + Dsjnt(A, B)

A: Consider the equation

Q: Let Aand B be non-empty sets such that |A|>|B|.If the number of elements in A∪Bis atmost 42 and at…

A: Let the number of elements in A is a , hence, |A|=a . Let the number of elements in B is b , hence,…

Q: А - (ВnС) %3D(А — В) n (А — С)

A:

Q: If a set B has 64 proper subsets of odd cardinality, what is |B|? O 6 O 7 O 8 O 9

A:

Q: The contiuum hypothesis: there exists cardinal number B such that No<ß<c صواب ihi

A: Ans : False , because

Q: 2- consider the set of all finite subsets of N, is this set countable or not, prove it?

A: Consider the set of all finite subsets of N, is this set countable or not, to prove it.

Q: Suppose that A and B are disjoint finite sets. Prove that AUB is finite.

A: Here are given sets A and B are finite sets. Then A=m, B=n  where m, n any fixed positive integer.…

Q: Indicate the cardinality of the set A, defined as the union of four sets of cardinalities 22, 31,…

A:

Q: 1.         Consider the sets: A = {a, b, c, d, e, f, h, j}, B = {a, b, i }, C = {f, h} and U =…

A: From the given information, the given sets are:

Q: Prove that [0,1] has the same cardinal number as [0,2] U[7,9].

A:

Q: 8. have a job}, draw a Venn diagram relating the two sets, giver that the universal set U={Human…

A:

Q: how that if |A| = |B| and |B| = |C| then |A| = |C|. The sets A, B, and C may be infinite, so ou must…

A:

Q: Show that the following pair of sets have the same cardinality. A = (5, 9] and B = (1, 2) ∪[4, 7]

A: Two sets A and B have the same cardinality provided there is a bijection from A to B.

Q: The Cartesian product of two sets containing five elements each has a cardinality of * O 16 Cannot…

A: Consider the given two sets which have each cardinality 5 Let set A=a,b,c,d,e and B=1,2,3,4,5

Q: What is the cardinal number for the set B = {four} ??

A: Cardinal number of a set is defined by the number of elements in the Set.

Q: Suppose we modify the construction of the Cantor set by starting with the open interval (0, 1) and…

A:

Q: (a) What is the cardinality of the interval (0, 1), finite, countably infinite, or uncountable? (b)…

A: Schroder-Bernstein Theorem: If there exists injective functions f : A→B and g : B→A between the sets…

Q: 20. What is the cardinality of each of these sets? а) и c) {Ø, {Ø}} b) {Ø} d) {Ø, {Ø}, {Ø, {Ø}}}

A:

Q: Determine the cardinality of each of the given sets: a) The set T of counting numbers that are…

A: The pair of sets are equivalent if there exists a bijection between then. We product the example of…

Q: how many subsets of {0,1 ....,9} have cardinality 4 or more?

A:

Q: Find the cardinal number of the set C={(1/x) ∣ x is an integer that's greater than or equal to 4…

A:

Q: 3. Prove that if A is a set then so is {A} but do NOT use an argument that involves stages…

A: Let A is any set then as every set is a subset of itself then, A⊆A⇒A∈PA⇒A∈PPA

Q: 6. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

A:

Q: is the set [5,100] compact?

A: Given that:A set is S=5,100.We have to check whether a set 5,100 is compact or not?

Q: Show that (B - A)U(C- A) = (BUC)- A 1) Using a Venn diagram 2) Using the definition of equal sets

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Q: Let S={1,2,3,4,5,6} How many subsets are there of cardinality 4?

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Q: Are the sets Z x Z; ((x.y): x*y?) closed in (R , | |) ? What about the sets (0,1]U(2,3); [0, 00) in

A:

Q: 2. Let U = {a, b, c, d, e, f, g, h} be the universal set, and let A = {b, c, d, f, g}, B = {a, b,…

A:

Q: Give an example of two sets A and B which are homeomorphic, A is complete and B is not.

A:

Q: 4. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

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Q: Suppose the universal set contains the natural numbers that are no more than 20. Sets A and B are…

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Q: Ifs is(finite or infinite) Contable Set then prove that M*(S) ==

A:

Q: 5. Deduce from (4) that the set {2} 2-: n = 1, 2, 3, ... is closed in R.

A: Given set  S =2 ∪2-1n  :  n=1  2,  3 , . . .

Q: what does R mean in R-C=C' , is that a universal set ?

A: Here R=universal set.   The Venn diagram of C is:   The Venn diagram of R - C is:

Q: How many subsets of {0,1,…,9} have cardinality 5 or more?

A: